Asymptotically good towers and differential equations

Peter Beelen; Irene I. Bouw

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Asymptotically good towers and differential equations

Peter Beelen·Irene I. Bouw

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Abstract

This paper concerns towers of curves over a finite field with many rational points, following Garcia--Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is the study of algebraic solutions to Fuchsian differential equations modulo $p$. We apply our results to towers of modular curves, and find new asymptotically good towers.

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Peter Beelen, Irene I. Bouw. 2004-05-24. Asymptotically good towers and differential equations. https://arxiv.org/abs/math/0405449

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